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A122885
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The (3,3)-entry in the n-th power of the 3 X 3 matrix M = [1,1,1; 4,2,1; 9,3,1].
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3
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1, 13, 61, 385, 2185, 12853, 74677, 435721, 2538625, 14798077, 86245741, 502684561, 2929845241, 17076419653, 99528607141, 580095354265, 3381043256305, 19706164707853, 114855943942237, 669429501042721
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n+1) = 4*a(n) + 11*a(n-1) - 2*a(n-2).
a(n)=-(45/68)*sqrt(2)*[3-2*sqrt(2)]^(n-1)+(33/34)*[3+2*sqrt(2)]^(n-1)+(45/ 68)*[3+2*sqrt(2)]^(n-1) *sqrt(2)+(33/34)*[3-2*sqrt(2)]^(n-1)-(16/ 17)*(-2)^(n-1), with n>=1 - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 09 2008
G.f.: x*(1+9*x-2*x^2)/((2*x+1) * (1-6*x+x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 12 2009]
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EXAMPLE
| M^2 * [0,0,1] = [3, 7, 13], so the right term in the last row is 13 = a(2).
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CROSSREFS
| Cf. A122883, A122884, A122886.
Sequence in context: A047673 A141725 A147185 * A135535 A158870 A145044
Adjacent sequences: A122882 A122883 A122884 * A122886 A122887 A122888
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KEYWORD
| nonn,easy
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AUTHOR
| Gary W. Adamson and Roger L. Bagula (qntmpkt(AT)yahoo.com), Sep 17 2006
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EXTENSIONS
| More terms from Paolo P. Lava (paoloplava(AT)gmail.com), Jul 09 2008
Definition replaced by a precise phrase by the Assoc. Editors of the OEIS, Mar 12 2010.
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